Abstract

We prove that for every countable dense subset D of a separable Hilbert space H\mathcal{H} there exists a continuous function with empty subdifferential at every point x outside D, meanwhile for every x in D the subdifferential at x is the whole space H\mathcal{H}.

Author information

Contact details are reproduced from the original publication and may be historical.

Juan Ferrera

Dep. de Análisis Matemático, Facultad Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain

ferrera@mat.ucm.es

Javier Gómez Gil

Dep. de Análisis Matemático, Facultad Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain

gomezgil@mat.ucm.es

Keywords

  • Van der Waerden function
  • Takagi function
  • subdifferential

Mathematics Subject Classification

26A27, 49J52

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Suggested citation

J. Ferrera, J. Gómez Gil. “Generalized Takagi-Van der Waerden Functions and their Subdifferentials.” Journal of Convex Analysis 25 (2018), No. 4, 1355–1369. https://doi.org/10.68381/jca25083

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.